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Mathematics and Computing 2013 pp 313–322Cite as

On Quasi-ideals in Ternary Semirings

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 91))

Abstract

In this paper, we study the concept of minimal quasi-ideals in ternary semiring and prove some standard results analogous to ring theory. We also introduced the concept of a \(Q\)-simple ternary semiring and \(0\)-\(Q\)-simple ternary semiring and characterize \(0\)-minimal quasi-ideals in terms of \(Q\)-simple ternary semiring.

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References

  1. Dutta, T.K., Kar, S.: On regular ternary semirings, advances in Algebra. In: Proceedings of the ICM Satellite Conference in Algebra and Related Topics, pp. 343–355. World Scientific, New Jersey (2003)

    Google Scholar 

  2. Dutta, T.K., Kar, S.: A note on regular ternary semiring. Kyungpook J. Math. 46, 357–365 (2006)

    Google Scholar 

  3. Iampan, A.: Characterization of ordered Quasi-ideals of ordered \(\Gamma \)-semigroups. Kragujevac J. Math. 35(1), 13–23 (2011)

    Google Scholar 

  4. Kar, S.: On quasi-ideals and bi-ideals in ternary semirings, Int. J. Math. Sci. 18, 3015–3023 (2005)

    Google Scholar 

  5. Lee, S.K., Kang, S.G.: Characterizations of regular po-semigroups. Comm. Korean Math. Soc. 14(4), 687–691 (1999)

    Google Scholar 

  6. Lehmer, D.H.: A ternary analogue of an Abelian groups. Am. J. Math. 59, 329 (1932)

    Google Scholar 

  7. Lister, W.G.: Ternary rings. Trans. Am. Math. Soc. 154, 37 (1971)

    Google Scholar 

  8. Steinfeld, O.: Quasi-ideals in Rings and Semigroups. Akademiai Kiado, Budapest (1978)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Scientific Analysis Group, Defence Research and Development Organisation, Delhi, 110054, India

    Manish Kant Dubey

  2. University of Delhi, Delhi, 110007, India

    Anuradha

Authors
  1. Manish Kant Dubey
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  2. Anuradha
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Corresponding author

Correspondence to Manish Kant Dubey .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  2. Dept of Computer Science & Engineering, Haldia Institute of Technology, Haldia, India

    Debasis Giri

  3. Ministry of Defence, Scientific Analysis Group, Defence Research and Development Organisation, New Delhi, Delhi, India

    P. K. Saxena

  4. Department of Mathematics, India Institute of Technology, Kharagpur, West Bengal, India

    P. D. Srivastava

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Dubey, M.K., Anuradha (2014). On Quasi-ideals in Ternary Semirings. In: Mohapatra, R., Giri, D., Saxena, P., Srivastava, P. (eds) Mathematics and Computing 2013. Springer Proceedings in Mathematics & Statistics, vol 91. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1952-1_21

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